(Left) An atomic force microscope image showing a sample of twisted layers of WS₂ (a material made of tungsten and sulfur). The scale bar represents 4 micrometers (4 millionths of a meter). (Right) A diagram showing how the Hall effect (a sideways voltage) was measured in the twisted material. The red arrow represents the path of electrons, while V0 and VH are the voltages applied and measured in the experiment. Credit: left, Yuzhao Zhao; right Judy Ji

In 2018, a discovery in materials science sent shock waves throughout the community. A team showed that stacking two layers of graphene—a honeycomb-like layer of carbon extracted from graphite—at a precise “magic angle” turned it into a superconductor, says Ritesh Agarwal of the University of Pennsylvania.

This sparked the field of “twistronics,” revealing that twisting layered materials could unlock extraordinary material properties.
Building on this concept, Agarwal, Penn theoretical physicist Eugene Mele, and collaborators have taken twistronics into new territory.
In a study published in Nature, they investigated spirally stacked tungsten disulfide (WS2) crystals and discovered that, by twisting these layers, light could be used to manipulate electrons. The result is analogous to the Coriolis force, which curves the paths of objects in a rotating frame, like how wind and ocean currents behave on Earth.
“What we discovered is that by simply twisting the material, we could control how electrons move,” says Agarwal, Srinivasa Ramanujan Distinguished Scholar in the School of Engineering and Applied Science. This phenomenon was particularly evident when the team shined circularly polarized light on WS2 spirals, causing electrons to deflect in different directions based on the material’s internal twist.
The origins of the team’s latest findings trace back to the early days of the COVID-19 pandemic lockdowns when the lab was shut down and first author Zhurun (Judy) Ji was wrapping up her Ph.D.
Unable to conduct physical experiments in the space, she shifted her focus to more theoretical work and collaborated with Mele, the Christopher H. Browne Distinguished Professor of Physics in the School of Arts & Sciences.

Together, they developed a theoretical model for electron behavior in twisted environments, based on the speculation that a continuously twisted lattice would create a strange, complex landscape where electrons could exhibit new quantum behaviors.
“The structure of these materials is reminiscent of DNA or a spiral staircase. This means that the usual rules of periodicity in a crystal—where atoms sit in neat, repeating patterns—no longer apply,” Ji says.
As 2021 arrived and pandemic restrictions lifted, Agarwal learned during a scientific conference that former colleague Song Jin of the University of Wisconsin-Madison was growing crystals with a continuous spiral twist. Recognizing that Jin’s spirally twisted WS2 crystals were the perfect material to test Ji and Mele’s theories, Agarwal arranged for Jin to send over a batch. The experimental results were intriguing.
Mele says the effect mirrored the Coriolis force, an observation that is usually associated with the mysterious sideways deflections seen in rotating systems. Mathematically, this force closely resembles a magnetic deflection, explaining why the electrons behaved as though a magnetic field were present even when there was none. This insight was crucial, as it tied together the twisting of the crystal and the interaction with circularly polarized light.
Agarwal and Mele compare the electron response to the classic Hall effect wherein current flowing through a conductor is deflected sideways by a magnetic field. But, while the Hall effect is driven by a magnetic field, here “the twisting structure and the Coriolis-like force were guiding the electrons,” Mele says.

“The discovery wasn’t just about finding this force; it was about understanding when and why it appears and, more importantly, when it shouldn’t.”
One of the major challenges, Mele adds, was that, once they recognized this Coriolis deflection could occur in a twisted crystal, it seemed that the idea was working too well. The effect appeared so naturally in the theory that it appeared hard to switch off even in scenarios where it shouldn’t exist. It took nearly a year to establish the exact conditions under which this phenomenon could be observed or suppressed.
Agarwal likens the behavior of electrons in these materials to “going down a slide at a water park. If an electron went down a straight slide, like conventional material lattices, everything would be smooth. But, if you send it down a spiraling slide, it’s a completely different experience. The electron feels forces pushing it in different directions and come out the other end altered, kind of like being a little ‘dizzy.'”
This “dizziness” is particularly exciting to the team because it introduces a new degree of control over electron movement, achieved purely through the geometric twist of the material. What’s more, the work also revealed a strong optical nonlinearity, meaning that the material’s response to light was amplified significantly.
“In typical materials, optical nonlinearity is weak,” Agarwal says, “but in our twisted system, it’s remarkably strong, suggesting potential applications in photonic devices and sensors.”

Another aspect of the study was the moiré patterns, which are the result of a slight angular misalignment between layers that plays a significant role in the effect. In this system, the moiré length scale—created by the twist—is on par with the wavelength of light, making it possible for light to interact strongly with the material’s structure.
“This interaction between light and the moiré pattern adds a layer of complexity that enhances the effects we’re observing,” Agarwal says, “and this coupling is what allows the light to control electron behavior so effectively.”
When light interacted with the twisted structure, the team observed complex wavefunctions and behaviors not seen in regular two-dimensional materials. This result ties into the concept of “higher-order quantum geometric quantities,” like Berry curvature multipoles, which provide insight into the material’s quantum states and behaviors.
These findings suggest that the twisting fundamentally alters the electronic structure, creating new pathways for controlling electron flow in ways that traditional materials cannot.
And finally, the study found that by slightly adjusting the thickness and handedness of the WS2 spirals, they could fine-tune the strength of the optical Hall effect. This tunability suggests that these twisted structures could be a powerful tool for designing new quantum materials with highly adjustable properties.
“We’ve always been limited in how we can manipulate electron behavior in materials. What we’ve shown here is that by controlling the twist, we can introduce completely new properties,” Agarwal says.
“We’re really just scratching the surface of what’s possible. With the spiral structure offering a fresh way for photons and electrons to interact, we’re stepping into something completely new. What more can this system reveal?”

More information:
Zhurun Ji et al, Opto-twistronic Hall effect in a three-dimensional spiral lattice, Nature (2024). DOI: 10.1038/s41586-024-07949-1

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Theoretical physicist uncovers how twisting layers of a material can generate mysterious electron-path-deflecting effect (2024, October 4)
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